Hacker's Delight

15-2. Comparing Floating-Point Numbers Using Integer Operations

One of the features of the IEEE encodings is that non-NAN values are properly ordered if treated as signed magnitude integers.

To program a floating-point comparison using integer operations, it is necessary that the “unordered” result not be needed. In IEEE 754, the unordered result occurs when one or both comparands are NaNs. The methods below treat NaNs as if they were numbers greater in magnitude than infinity.

The comparisons are also much simpler if −0.0 may be treated as strictly less than +0.0 (which is not in accordance with IEEE 754). Assuming this is acceptable, the comparisons may be done as shown below, where and denote floating-point comparisons, and the ≈ symbol ...